On Pole Placement and Invariant Subspaces

The classical eigenvalue assignment problem is revisited in this note. We derive an analytic expression for pole placement which represents a slight generalization of the celebrated Bass-Gura and Ackermann formulae, and also is closely related to the modal procedure of Simon and Mitter.Comment: Presented at ICAT201

Development and characterization of sulfonated polysulfone membrane for proton exchange membrane fuel cell (PEMFC)

Sulfonated polysulfone membranes with varying degree of sulfonation have been successfully synthesized by electrophilic substitution via sulfonation process in this study. Sulfonated dense membranes were fabricated using locally available pneumatically controlled casting machine. Characterizations of different degree of sulfonated polysulfone membranes were conducted through swelling effects, ion exchange capacity (IEC), Thermal Gravimetric Analysis (TGA), Differential Scanning Calorimeter (DSC), X-ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and proton conductivity measurement. It was observed that an increase in the degree of sulfonation increases the water uptake of the membranes and sulfonic acid group in the polymer membrane. From FTIR, it was clearly confirmed the occurrence of sulfonation in the polymer structure as the evidence of the SO3 stretching band was noticed at frequency of 1027 cm-1. It was found from TGA that the sulfonic acid group started to decompose at 250ºC and decomposition of the polymer main chain decreases by increasing the degree of sulfonation. The Tg value detected in this study was increased accordingly with the degree of sulfonation though some hindrance was found to decrease the Tg value during the experiments. Proton conductivity measurement of sulfonated polysulfone membrane was found to increase with operating temperature and degree of sulfonation. It was found that at higher temperature (80ºC), SPSU10 membrane exhibits proton conductivity value at par with that of Nafion 117 membrane. It was also observed from XRD analysis that dimethylformamide solvent was prone to form hydrogen bonding with sulfonic groups hence allows formation of a more regular structure which leads to an incipient crystalline character of the material structure. SEM micrographs showed clearly the altered microstructure of polysulfone polymer before and after the sulfonation process

Lack of Finite Characterizations for the Distance-based Revision

Lehmann, Magidor, and Schlechta developed an approach to belief revision based on distances between any two valuations. Suppose we are given such a distance D. This defines an operator |D, called a distance operator, which transforms any two sets of valuations V and W into the set V |D W of all elements of W that are closest to V. This operator |D defines naturally the revision of K by A as the set of all formulas satisfied in M(K) |D M(A) (i.e. those models of A that are closest to the models of K). This constitutes a distance-based revision operator. Lehmann et al. characterized families of them using a loop condition of arbitrarily big size. An interesting question is whether this loop condition can be replaced by a finite one. Extending the results of Schlechta, we will provide elements of negative answer. In fact, we will show that for families of distance operators, there is no "normal" characterization. Approximatively, a normal characterization contains only finite and universally quantified conditions. These results have an interest of their own for they help to understand the limits of what is possible in this area. Now, we are quite confident that this work can be continued to show similar impossibility results for distance-based revision operators, which suggests that the big loop condition cannot be simplified

On the Mixing of Diffusing Particles

We study how the order of N independent random walks in one dimension evolves with time. Our focus is statistical properties of the inversion number m, defined as the number of pairs that are out of sort with respect to the initial configuration. In the steady-state, the distribution of the inversion number is Gaussian with the average <m>~N^2/4 and the standard deviation sigma N^{3/2}/6. The survival probability, S_m(t), which measures the likelihood that the inversion number remains below m until time t, decays algebraically in the long-time limit, S_m t^{-beta_m}. Interestingly, there is a spectrum of N(N-1)/2 distinct exponents beta_m(N). We also find that the kinetics of first-passage in a circular cone provides a good approximation for these exponents. When N is large, the first-passage exponents are a universal function of a single scaling variable, beta_m(N)--> beta(z) with z=(m-<m>)/sigma. In the cone approximation, the scaling function is a root of a transcendental equation involving the parabolic cylinder equation, D_{2 beta}(-z)=0, and surprisingly, numerical simulations show this prediction to be exact.Comment: 9 pages, 6 figures, 2 table

Preferential and Preferential-discriminative Consequence relations

The present paper investigates consequence relations that are both non-monotonic and paraconsistent. More precisely, we put the focus on preferential consequence relations, i.e. those relations that can be defined by a binary preference relation on states labelled by valuations. We worked with a general notion of valuation that covers e.g. the classical valuations as well as certain kinds of many-valued valuations. In the many-valued cases, preferential consequence relations are paraconsistant (in addition to be non-monotonic), i.e. they are capable of drawing reasonable conclusions which contain contradictions. The first purpose of this paper is to provide in our general framework syntactic characterizations of several families of preferential relations. The second and main purpose is to provide, again in our general framework, characterizations of several families of preferential discriminative consequence relations. They are defined exactly as the plain version, but any conclusion such that its negation is also a conclusion is rejected (these relations bring something new essentially in the many-valued cases).Comment: team Logic and Complexity, written in 2004-200

Mutual Fund Performance in Pakistan, 1995-2004

Mutual funds are the most popular vehicle of investing in the stock market and their performance evaluation is a topic dear to both investors and academics. Surprisingly, mutual funds have not played a very important role in the Pakistani stock market and perhaps consequently almost nothing has been written about their performance in any academic journal. This paper looks at the performance of Pakistani mutual funds over the last five and ten year periods using Sharpe, Jensen and Treynor measures of portfolio performance analysis. The performance is compared to that of the market portfolio defined as the KSE 100 index. Using the Sharpe measure the performance of virtually all the funds was found to be inferior to that of the market portfolio. The Jensen and Treynor measures showed about half the funds to be outperforming the market portfolio over the last five years, but when the risk measure was corrected using Famas net selectivity measure the market portfolio outperformed all the funds except one. These results support the semi-strong form of market efficiency hypothesis even more strongly than it has been demonstrated in the developed markets.Mutual fund performance, Sharpe Jensen and Treynor measures of portfolio performance, test of semi-strong form of market efficiency